continued fraction

American  

noun

Mathematics.

1. a fraction whose denominator contains a fraction whose denominator contains a fraction, and so on.

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continued fraction British  

noun

1. a number plus a fraction whose denominator contains a number and a fraction whose denominator contains a number and a fraction, and so on

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Etymology

Origin of continued fraction

First recorded in 1860–65

Example Sentences

These latest projects are primarily driven by a specific continued fraction whose nested integers form the sequence 1, 2, 3,…, Elsner says.

From Scientific American • Jun. 2, 2023

There is another type of continued fraction called the ascending continued fraction, the type so far discussed being called the descending continued fraction.

From Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 2 "Constantine Pavlovich" to "Convention" by Various

The Incommensurability of Infinite Continued Fractions.—There is no general test for the incommensurability of the general infinite continued fraction.

From Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 2 "Constantine Pavlovich" to "Convention" by Various

“If in the infinite continued fraction of the second class an ≥ bn + 1 for all values of n, it converges to a finite limit not greater than unity.”

From Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 2 "Constantine Pavlovich" to "Convention" by Various

The method is theoretically very elegant, but the disadvantage is that it gives the result in the form of a continued fraction, which for the most part must ultimately be converted into a decimal.

From Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 7 "Equation" to "Ethics" by Various